Watch a 46-minute mathematics lecture exploring the fascinating asymptotic phenomena in random dimer coverings of large planar graphs, with particular focus on the Aztec diamond family of subgraphs within periodically weighted square lattices. Delve into how these dimer configurations create distinct frozen regions and various phases in unfrozen areas, while discovering their precise mathematical description through the geometry of underlying Riemann surfaces. Learn from MIT professor Alexey Borodin as he presents collaborative research with T. Berggren and M. Duits at the Institut des Hautes Etudes Scientifiques (IHES), demonstrating how surface structure influences dimer statistics.